What is the meaning of "two or more letters audibly emitted therefrom"? And how should a prayer in which such a low sound was emitted during prostration be judged, and is it obligatory to re-pray three full days as a compensatory measure for that?

Laughter invalidates the prayer if two or more letters become audible, or if it is a guffaw, even if two letters are not audible. "Two letters become audible" means uttering two letters from the alphabet.

If the worshiper doubts whether two letters became audible or not, the default is the validity of the prayer, not its invalidation. He is not required to do anything, especially if he is prone to whispers (waswas).

However, if the worshiper is certain that two letters became audible, then he must re-pray. There is no difference whether the sound was loud or low.

If the prayer was from a single day and the worshiper knows which specific prayer it was—Dhuhr, Asr, Maghrib, or Isha—he should re-pray it. If he has forgotten which specific prayer was invalidated, he should re-pray five prayers, starting from Dhuhr and ending with Fajr, as his obligation is not discharged otherwise.